On 01/03/2013 3:11 AM, Alan Smaill wrote:> Nam Nguyen <namducnguyen@shaw.ca> writes:>>> On 28/02/2013 7:51 PM, Virgil wrote:>>> In article <khUXs.345339$pV4.177097@newsfe21.iad>,>>> Nam Nguyen <namducnguyen@shaw.ca> wrote:>>>>>>> On 28/02/2013 8:27 AM, Frederick Williams wrote:>>>>> Nam Nguyen wrote:>>>>>>>>>>>> On 27/02/2013 10:12 PM, Virgil wrote:>>>>>>> In article <R8AXs.345282$pV4.85998@newsfe21.iad>,>>>>>>>>>>>> The set of all functions from |N = {0,1,2,3,...} to {0,1,2,...,9} with>>>>>>> each f interpreted as Sum _(i in |N) f(i)/10^1, defines such a>>>>>>> structure..>>>>>>>>>>>> That doesn't look like a structure to me. Could you put all what>>>>>> you've said above into a form using the notations of a structure?>>>>>>>>>> There is a set and a collection of functions on it. How does it fail to>>>>> be a structure?>>>>>>>> From what textbook did you learn that a structure is defined as>>>> "a set and a collection of functions on it"?>>>>>> Then give us your textbook definition of structure and show why the>>> above fails to meet it.>>>> Shoenfield, Section 2.5 "Structures". One reason the above fails is,>> you don't define, construct, the predicate (set) for the symbol '^'.>> Who said that that is a predicate here?

In a structure, a function is a special predicate: all of whichare just _sets of n-tuples_ .

>>> And that's just 1 reason amongst others. Do you admit it now that>> the above fails to meet the requirements of a language structure?>> It fits with Shoenfield in the case where the only predicate> is equality.

As just mentioned, you still have to construct that specialpredicate set for the symbol '^'. To be precise of course.

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